Sick Burn is a status generated due to the assault from Problem Sleuth's Poison Pen Letter Battle technique. It's never dictated exactly what the Sick Burn does, but Problem Sleuth engages his Pax Probliscum attack immediately afterward; This immediately demolishes another Health Bar, suggesting that it weakens Demonhead Mobster Kingpin's defenses toward Sepulchritude-type attacks.
Sick Burn was mentioned again in Homestuck, in which, after delivering some SICK RHYMES
upon Dave, Tavros Nitram was shown with the caption "you just started some SICK FIRES, BRO".
Sometime after dying, a Dead Tavros meets a Dead Dave in person in the dream bubbles, later conjuring some truly unhealthy incendiaries in above average need for medical attention.